Potts had replaced Jack Collison just after the hour mark at the Emirates Stadium, but suffered a nasty concussion following a heavy fall after an accidental aerial collision with Bacary Sagna.
The 18-year-old spent the night in hospital and underwent further scans and tests on Thursday, which came back positively. Potts has expressed his gratitude for the messages of support he has received and will undergo a period of rest before being allowed to resume light training in the gym.
FIFA president Sepp Blatter had earlier expressed his backing for Potts, writing on Twitter: "Best wishes & quick recovery to @DanPotts03. Concussion in football is a big issue that FIFA is taking very seriously."
Meanwhile, Collison believes West Ham will learn some hard lessons from their 5-1 mauling. The Irons were torn apart by a rampant Gunners side who ran in four goals in the space of 10 minutes at the start of the second half.
Things had started well for the visitors, who weathered early Arsenal pressure to take the lead after 18 minutes when Collison crashed in a 20-yard effort following a corner. However, Lukas Podolski's fine strike sent the sides in level at the break and Arsenal came out on fire following the restart.
Olivier Giroud clipped the ball home at the near post before Podolski set up Santi Cazorla, while Theo Walcott and Giroud again put the home side out of sight before the hour.
From then on it was a case of damage limitation for West Ham, but Collison feels the squad will use their break from FA Cup action this weekend to focus on putting things right in their next Premier League outing at Craven Cottage.
"We defended well in the first half and created a couple of chances," Collison said. "Then we had 10 minutes of poor defending and when you do that against a team like Arsenal, they are going to cut you open.
"As a team, we know that is not good enough and it is up to us to pick ourselves up. The manager has not got to tell us it was not good enough, we know that. We have to get ourselves back up and go for the Fulham game."